What is the derivative of (x+2e^{-x}) ?

The derivative of (x+2e^{-x}) is -e^{-x}x-e^{-x}

What is the first derivative of (x+2e^{-x}) ?

The first derivative of (x+2e^{-x}) is -e^{-x}x-e^{-x}

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\frac{d}{d x} ((x + 2) e^{- x})

- e^{- x} x - e^{- x}

Solution steps

\frac{d}{d x} ((x + 2) e^{- x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + 2, g = e^{- x}

= \frac{d}{d x} (x + 2) e^{- x} + \frac{d}{d x} (e^{- x}) (x + 2)

\frac{d}{d x} (x + 2) = 1

\frac{d}{d x} (e^{- x}) = - e^{- x}

= 1 \cdot e^{- x} + (- e^{- x}) (x + 2)

Simplify

1 \cdot e^{- x} + (- e^{- x}) (x + 2) : - e^{- x} x - e^{- x}

= - e^{- x} x - e^{- x}

\frac{d y}{d x} = \frac{x}{34 + x ^{2}}

\frac{d y}{d x} = 9 y e^{x + 3}

\int \frac{3 + 16 x}{8 x - 4} d x

\frac{d}{d x} (- \frac{x}{4} + \frac{3}{4})

\int x^{2} e^{- 2 x} d x

What is the derivative of (x+2e^{-x}) ?
The derivative of (x+2e^{-x}) is -e^{-x}x-e^{-x}
What is the first derivative of (x+2e^{-x}) ?
The first derivative of (x+2e^{-x}) is -e^{-x}x-e^{-x}